Question

Find the equation of the line through the point (3, 6) that makes an angle tan−1(3) with the x-axis.

A) y=3x+3
B) y=3x−6
C) y=−3x+6
D) y=−3x−3

Answer 1

The equation of the line through the point (3, 6) that makes an angle tan−1(3) with the x-axis is y = 3x - 3.

Step-by-step explanation:

To find the equation of a line through the point (3, 6) that makes an angle of tan-1(3) with the x-axis, we need to determine the slope of the line. The slope of a line is given by the tangent of the angle it makes with the x-axis. Using the given angle, the slope is tan(tan-1(3)) or 3.

Since the line passes through the point (3, 6), we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where x1 = 3, y1 = 6, and m = 3 (the slope).

Plugging in the values, we get y - 6 = 3(x - 3), which simplifies to y = 3x - 9 + 6. Simplifying further, we get y = 3x - 3. Therefore, the equation of the line is y = 3x - 3.